Question

Reshanda bought 17 plants to arrange along the border of her garden. How many distinct arrangements can she make if the plants are comprised of 6 tulips, 5 roses, and 6 daisies?

Answer 1

Given the word problem, we can deduce the following information:

1. Reshanda bought 17 plants to arrange along the border of her garden.

2. The plants are comprised of 6 tulips, 5 roses, and 6 daisies.

To determine the distinct arrangements that can she make, we use permutation as it an arrangement of objects in a definite order. The process is shown below:

$Arrangements=\frac{n!}{p_1!p_2!p_3!}$

where:

n=number of different objects=17

p1=objects of the first kind=6

p2=objects of the second kind=5

p3=objects of the third kind=6

We plug in what we know:

$\begin{gathered} Arrangements=\frac{n!}{(p_{1})!(p_{2})!(p_{3})!} \\ =\frac{17!}{6!5!6!} \\ Calculate \\ Arrangements=5717712 \end{gathered}$

Therefore, the answer is 5717712 arrangements.